Second Workshop on Spatial Stochastic Models for Wireless Networks

Research Article

Navigation on Self-Organized Networks

  • @INPROCEEDINGS{10.1109/WIOPT.2006.1666522,
        author={Charles  Bordenave},
        title={Navigation on Self-Organized Networks},
        proceedings={Second Workshop on Spatial Stochastic Models for Wireless Networks},
        publisher={IEEE},
        proceedings_a={SPASWIN},
        year={2006},
        month={8},
        keywords={},
        doi={10.1109/WIOPT.2006.1666522}
    }
    
  • Charles Bordenave
    Year: 2006
    Navigation on Self-Organized Networks
    SPASWIN
    IEEE
    DOI: 10.1109/WIOPT.2006.1666522
Charles Bordenave1,*
  • 1: Ecole Normale Superieure and INRIA
*Contact email: charles.bordenave@ens.fr

Abstract

On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on Rd. We examine the distribution of stable functionals, the local weak convergence of the navigation tree, the asymptotic average of a functional along a path, the shape of the navigation tree and its topological ends. We illustrate our work in the small world graphs, and new results are established. This work is motivated by applications in computational geometry and in self-organizing networks.